Objectives: Students will be introduced to log functions and learn how to use them as an algebraic tool in solving for the variable in an equation involving an exponential function.
Preliminaries/Lead-In: When we get to Chapter Four, I always like to talk about the fact that we are now going to learn about another class of functions - logarithms - but this time not as potential models (I don't have a great explanation for why we don't learn to model logarithmic data - it's just a choice we make in this course based upon prevelance). Instead (as Mairead highlights below) we learn about logarithms to give ourselves (1) an important algebraic tool, and later (2) another modeling tool for exponential and power data.
Suggested Procedures: I will have them work on question 1 in small groups and then come together and discuss what they figure out for that. Then I will start 2 together as a class and let them finish it in small groups. I will then come together to check what they have done. Then I will let them work on Q3 in small groups. I will repeat the process for natural log - although I will probably let them do more of that by themselves - keeping track of how everyone does. I expect to get thru to Q5 in the first class and then start the second class with Q6. I may have to send them away to finish some of 1-5 if I don't get thru it all and talk about it at the beginning of the next class. Q6 has to be completed together as a class and then I have them take some time to check some of those rules - showing some of them how to do that. Then we will finish the second day by giving them time to work on Q7 discussing as they go along - I will need to help them with half-life and double time before they get to the last two parts of (d) as this is the first time we will use these terms.
Wrap-Up/Take-Away: The main thing to take away from this activity is that we now have an algebraic tool to deal with equations involving an exponential function.
Possible Homework: I'm not sure if I will collect this activity to grade or not but if I do then I will probably give until the next class to have it ready to hand in.
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